Ray Optics and Optical Instruments

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the curved surfaces 20 cm each is immersed in a liquid of refractive index nL. The correct plot showing the variation of the power, in the units of diopter (D), as a function of nL is:

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence 0. The ray partially refracts into the sphere with angle of refraction 0 and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is . Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

1. P → 5; Q → 2; R → 1; S → 4
2. P → 5; Q → 1; R → 2; S → 4
3. P → 3; Q → 2; R → 1; S → 4
4. P → 3; Q → 1; R → 2; S → 5

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of h (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct? [figure]

1. For n=1.42, h=50 cm.
2. For n=1.35, h=36 cm.
3. For n=1.45, h=65 cm.
4. For n=1.48, h=85 cm.